In this paper we study Clifford and harmonic analysis on some conformal flatspin manifolds. In particular we treat manifolds that can be parametrized by $U/ \Gamma$ where $U$ is a simply connected subdomain of either $S^{n}$ or$R^{n}$ and $\Gamma$ is a Kleinian group acting discontinuously on $U$.Examples of such manifolds treated here include for example $RP^{n}$ and$S^{1}\times S^{n-1}$. Special kinds of Clifford-analytic automorphic formsassociated to the different choices of $\Gamma$ are used to construct Cauchykernels, Cauchy Integral formulas, Green's kernels and formulas together withHardy spaces, Plemelj projection operators and Szeg\"{o} kernels for $L^{p}$spaces of hypersurfaces lying in these manifolds.
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机译：在本文中，我们研究了一些共形扁平旋转歧管上的Clifford和谐波分析。特别地，我们处理可以由$ U / \ Gamma $参数化的流形，其中$ U $是$ S ^ {n} $或$ R ^ {n} $的简单连接子域，而$ \ Gamma $是Kleinian组不连续地作用于$ U $。此处处理的此类歧管的示例包括$ RP ^ {n} $和$ S ^ {1} \ x S ^ {n-1} $。与$ \ Gamma $的不同选择相关联的特殊种类的Clifford解析自同构形式用于为$ L ^构造Cauchykernels，Cauchy积分公式，Green的核和公式以及Hardy空间，Plemelj投影算子和Szeg \“ {o}核{p}位于这些流形中的超曲面的空间。
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